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Eugine_Nier comments on AALWA: Ask any LessWronger anything - Less Wrong
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Well, with respect to mathematics at least one difference between the Greeks and everybody else, is that the Greeks provided proofs of the non-obvious results.
Yes, though that really got started with Euclid, who post-dates Aristotle. It's with Plato and Aristotle that the Greeks really set them-selves apart. I don't think we'd be reading any of the rest of it if it weren't for them.
Euclid is merely the first whose work has survived to the modern day. If tradition is to be believed, Thales and Pythagoras provided proofs of non-intuitive results from intuitive one. Furthermore, Hippocrates of Chios wrote a systematic treatment starting with axioms. All three predated Plato.
That's a good point about Hippocrates, I'd forgotten about him. Do you have a source handy on Thales and Pythagoras? I don't doubt it, it's just a gap I should fill. So far as I remember, a proof that the square root of two is irrational came out of the Pythagorean school, but that's all I can think of. I hadn't heard anything like that about Thales.
I linked to the relevant Wikipedia articles in my comment.
Ah, but note the 'history' section of the Thales article. It rather supports my picture, if it supports anything at all.
Why? If you mean that Thales learned the result from the Babylonians, the point is that he appears to have been the first to bother proving it.